Evaluating Flow in Fractal-Fracture Networks: Effect of Variable Aperture
2021
Abstract. While fractal models are often employed for describing the
geometry of fracture networks, a constant aperture is mostly assigned to all
the fractures when such models are flow simulated. In nature however, almost
all fracture networks exhibit variable aperture values and it is this
fracture aperture that controls the conductivity of individual fractures as
described by the well-known cubic-law. It would therefore be of practical
interest to investigate flow patterns in a fractal-fracture network where
the apertures scale in accordance to their position in the hierarchy of the
fractal. A set of synthetic fractal-fracture networks and two well-connected
natural fracture maps that belong to the same fractal system are used for
this purpose. A set of dominant sub-networks are generated from a given
fractal-fracture map by systematically removing the smaller fracture
segments with narrow apertures. The connectivity values of the
fractal-fracture networks and their respective dominant sub-networks are
then computed. Although a large number of fractures with smaller aperture
are eliminated, no significant decrease is seen in the connectivity of the
dominant sub-networks. A streamline simulator based on Darcy's law is used
for flow simulating the fracture networks, which are conceptualized as
two-dimensional fracture continuum models. A single high porosity value is
assigned to all the fractures. The permeability assigned to fractures within
the continuum model is based on their aperture values and there is nearly no
matrix porosity and permeability. The recovery profiles and time-of-flight
plots for each network and its dominant sub-networks at different time steps
are compared. The results from both the synthetic networks and the natural
data show that there is no significant decrease in fluid recovery in the
dominant sub-networks compared to their respective parent fractal-fracture
networks. It may therefore be concluded that in the case of such
hierarchical fractal-fracture systems with scaled aperture, the smaller
fractures do not significantly contribute to connectivity or fluid flow. In
terms of decision making, this result will aid geoscientists and engineers
in identifying only those fractures that ultimately matter in evaluating the
flow recovery, thus building models that are computationally less expensive
while being geologically realistic.
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